Semi-bluffing is a powerful tool in poker. It's important to learn when to use it and how to use it correctly. Bluffing and semi-bluffing bring us into the world of fold equity. Fold equity is a term we use to describe what we gain when our opponent folds. Our opponent can only fold after we've shown aggression by either betting or raising. Fold equity gives us more than one way to win a pot. We can make the best hand, or our opponent can fold. Semi-bluffing is when you're betting with a hand you doubt is good right now but has a good chance to improve on a later street. Because of this, you cannot semi-bluff on the river. Let's begin by looking at an example.
We have a 100x stack and hold AQ on the button in a 100NL game. An early position player limps, and we raise to $4. The big blind started with $40 and calls. The limper folds. The flop is 793. The pot is $9. The big blind has $36 left. We decide to bet $9, and he calls. The pot is now $27, and the big blind has $27 left. The turn is the K. The big blind bets out for $12.
As we examine our pot odds, we can see he bet just under 1/2 pot, which means we're getting a little better than 3:1 and need to have greater than about 23% equity to continue in the hand. Let's make some assumptions about his range to see how we're doing against that assumed range. Let's say we assume his range to be AK, 88, TT and 89s.
Let's do a quick exercise to estimate our equity against that range. We’ll analyze his hand range: 9 combinations of AK, 12 total combinations of 88 and TT, and 3 combinations of 89s. These hands divide well into two groups.
- Group 1: Against 88, TT, and 89s, we have roughly 15 outs with 1 card to come for an estimated 30% equity.
- Group 2: Against AK, we only have roughly the 9 flush outs for a total of 18% equity.
So, the 2 groups are 30% equity and 18% equity. Notice the 30% equity group contains 15 combinations, and the 18% equity group contains 9 combinations. So, the 30% group "weighs" quite a bit more than the 18% group. I'd use the MS Method here to find about 2/3 the way up from 18 to 30. The exact middle I know is 24, so I'd slide it a bit higher than that and estimate about 27% equity against this range. If you put this in Pokerstove, you'll find it gives us 28% equity. We're close, and close will do just fine.
Remember we needed 23% to call his bet, so we have the immediate odds to call his turn bet. Against his AK, it's likely we even make more money on the river as well, so there are some implied odds to consider. But, we can call without even considering implied odds.
However, we always need to make sure we consider all our options. We can fold. The EV of folding is always 0, so we know that's already worse than calling and out of the question. We can call, and we already explored that briefly. But, we can also raise. We can even raise to different amounts. Remember, only through aggression can we take advantage of fold equity.
We can minraise or shove and every amount in between. This aggression will give us more than one way to win the hand. We can make the best hand for showdown, or he can fold. Let's look at shoving.
First, let's make some assumptions about how he'll respond to a shove with his range. Let's say he'll call with AK and TT, but will fold 88 and 89s. There are 15 combinations he calls with, and 9 combinations he folds. So, he folds 37% of the time.
We have about $87 left in our stack, but our stack doesn't matter here because the big blind has less money than we do. He had $27 left in his stack on the turn and then bet $12. So, he now has $15 left. There is currently $39 in the pot. We can move all-in, which will risk $27 to win the current $39 pot. We need to him to fold about 40% of the time. He's only folding 37% of the time. Does that mean raising is not good? No. Here we have showdown equity in the hand to go along with our fold equity. Let’s look at a detailed way to figure out how often he needs to fold when we shove. If this look complicated, do not be concerned.
Fold%(pot won when he folds) + Call%(amount we win/lose when he calls)
Here we’re going to let x equal the percentage of times he folds.
x($39) + (1-x)(0.24($54) + 0.76(-$27)) > 0
39x + (1-x)($12.96 – $20.52) > 0
39x + (1-x)(-7.56) > 0
39x – 7.56 + 7.56x > 0
46.56x > 7.56
x > 0.1624
He has to fold more than 16% of the time in order for our shove to be +EV. Here we can plug in the percentages.
0.1624($39) + 0.8376(0.24($54) + 0.76(-$27)) > 0
$6.33 + 0.8376($12.96 – $20.52) > 0
$6.33 + 0.8376(-$7.56) > 0
$6.33 – $6.33 > 0
Our work checks out. Notice he is folding 37% of the time, and we only needed him to fold 16%. So, obviously the shove is +EV. Let’s look at the EV of this shove.
0.37($39) + 0.63(0.24($54) + 0.76(-$27)) = EV
$14.43 + 0.63(-$7.56) = EV
$14.43 – $4.76 = $9.67
Let’s compare this to the EV of the calling.
0.28($39) + 0.72(-$12) = EV
$10.92 – $8.64 = $2.28
So, we can see the power of the semi-bluff here. We often win the whole pot uncontested, and when we do win on the river if he calls, we win a bigger pot. There are three key variables when analyzing whether or not a semi-bluff shove is a good move.
- The size of the pot in relation to the money left. The larger the stack to pot ratio, the more often he must fold. This is because we're proportionally risking more.
- How often he folds. Normally the smaller the stack to pot ratio, the less often he'll fold and vice versa. This is because our opponent is normally aware of the reward to risk ratio to some extent.
- Your showdown equity. The more showdown equity you have, the less often he'll have to fold.